TORONTO, April 24 (Reuters) - The Canadian dollar edged higher against its U.S. counterpart on Tuesday, but held near an earlier three-week low as higher U.S. Treasury yields supported recent gains for the greenback.

The U.S. dollar reached its highest intraday in more than three months against a basket of major currencies as the 10-year Treasury yield broke above the psychologically significant barrier of 3 percent for the first time since January 2014.

Higher U.S. yields reflect investor expectations for additional interest rate hikes from the Federal Reserve. In contrast, investors have been dialing back expectations for further tightening from the Bank of Canada after the central bank held its benchmark interest rate steady at 1.25 percent last week and said it did not know when or how aggressive it would need to be to keep inflation in check.

“It does feel that it’s more of a rate call than an oil call on the (Canadian) dollar these days,” said Greg Taylor, Portfolio Manager at Redwood Asset Management. “We would have expected the Canadian dollar to do a little better given the move in oil we’ve had.”

U.S. crude oil futures settled 1.4 percent lower at $67.70 a barrel as concerns faded over the possibility that the United States might reinstate sanctions against Iran.

Still, oil has climbed as much as 19.8 percent since February.

At 4 p.m. EDT (2100 GMT), the Canadian dollar was trading 0.2 percent higher at C$1.2823 to the greenback, or 77.98 U.S. cents.

The currency’s strongest level of the session was C$1.2814, while it touched its weakest since April 3 at C$1.2860.

The modest gain for the loonie came after U.S. President Donald Trump said that a new North American Free Trade Agreement could be agreed quickly and as Canada hailed progress on forging new rules for the auto industry, the pivotal issue in talks to revamp the 24-year-old accord.

Canadian government bond prices were higher across the yield curve, with the two-year up 1 Canadian cent to yield 1.914 percent and the 10-year rising 5 Canadian cents to yield 2.348 percent.

The gap between the 10-year yield and its U.S. counterpart widened by 3.3 basis points to a spread of -65.2 basis points, its widest since March 29. (Reporting by Fergal Smith Editing by Susan Thomas and Sandra Maler)